We present an analysis of Bernstein's batch integer smoothness test
when applied to the case of polynomials over a finite field $\mathbb{F}_q.$ We
compare the performance of our algorithm with the standard method
based on distinct degree factorization from both an analytical and a
practical point of view. Our results show that although the batch
test is asymptotically better as a function of the degree of the
polynomials to test for smoothness, it is unlikely to offer
significant practical improvements for cases of practical interest.